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Find the perimeter of the rectangle whose length is $24 cm$ and the diagonal is $30 cm$ .

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84 cm

42 cm

54 cm

108 cm

answer is A.

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Detailed Solution

The following information is given:
Length of rectangle

(l)

is 24 cm.
Length of diagonal

(d)

is 30 cm.
Let the length of breadth be

b

.
Required formula to calculate the diagonal of the rectangle.

d = \sqrt{b^{2} + h^{2}}

………………… (1)
Substitute the values in equation (1).

\Rightarrow 30 = \sqrt{b^{2} + {(24)}^{2}}

\Rightarrow {(30)}^{2} = b^{2} + {(24)}^{2}

\Rightarrow 900 = b^{2} + 576

⇒

b^{2} = 900 - 576

⇒

b^{2} = 324

⇒

b = \pm 18

cm
Since the breath cannot be negative. So, neglect the negative value of breadth.
Hence, the breadth of the rectangle is

18

cm.

Perimeter of rectangle = 2 (l + b)

…………(2)
where, l and b are the length and breadth of the rectangle respectively.

Perimeter = 2 (24 + 18)

\Rightarrow

Perimeter

= 2 (42)

\Rightarrow

Perimeter

= 84

cm
Thus, the perimeter of rectangle is

84

cm.
Hence, the correct option is 1.

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